Subtract the following rational expressions. $\dfrac{19m+3m^3}{14m-3}-\dfrac{12m^2+3m}{14m-3}=$
Answer: We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{19m+3m^3}{14m-3}-\dfrac{12m^2+3m}{14m-3} \\\\ &=\dfrac{(19m+3m^3)-(12m^2+3m)}{14m-3} \\\\ &=\dfrac{19m+3m^3-12m^2-3m}{14m-3} \\\\ &=\dfrac{3m^3-12m^2+16m}{14m-3} \end{aligned}$ In conclusion, $\dfrac{19m+3m^3}{14m-3}-\dfrac{12m^2+3m}{14m-3}=\dfrac{3m^3-12m^2+16m}{14m-3}$